# If R is an integral domain with unit element, prove that any unit in R[x] must already be a unit in R.

Modern Algebra

Ring Theory (XL)

Polynomial Rings over Commutative rings

Integral Domain

Unit Element

Unit of a Commutative Ring

If R is an integral domain with unit element, prove that any unit in R[x] must already be a unit in R.

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This solution is comprised of a detailed explanation of Polynomial Rings over Commutative Rings.It contains step-by-step explanation that if R is an integral domain with unit element, then any unit in R[x] must already be a unit in R.

Solution contains detailed step-by-step explanation.

If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

Modern Algebra

Ring Theory (XLI)

Polynomial Rings over Commutative rings

Integral Domain

Unit Element

Unit of a Commutative Ring

If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

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